Question

A number is equal to twice a smaller number plus 3. The same number is equal to twuce the sum of the smaller number and 1. How many solutions are possible for this situation

Answer 1

Answer:

No solution

Step-by-step explanation:

Suppose the number is $y$ so ($y = ...$).

Now $y$ is equal to twice a smaller number plus 3. Assuming the smaller number as $x$, we can write it as:

$y = 2x + 3$ --- (1)

Also, the same number $y$ is equal to twice the sum of smaller number and 1:

$y=2x+1$ --- (2)

Now for both of these equations, we need to find a point which satisfies them.

For example, for equation 1, take $y=5$ which means $2(1) + 3$ so the solution will be (1, 3).

Substituting the same value of y here in equation 2:

$5=2(2)+1$ so the solution for this will be (2, 5).

It means that there is no such point which can satisfy both the equations. Hence, there is no solution possible for these two equations.

Answer 2

Answer: The system of equations HAS NO SOLUTION.

Step-by-step explanation:

Let be "y" the first number and "x" the smaller number.

Since the first number  is equal to twice a smaller number plus 3, then:

$y=2x+3$  (Equation 1)

Since the same number is equal to twice the sum of the smaller number and 1, then:

$y=2(x+1)$

$y=2x+2$  (Equation 2)

We need to remember that the equation of the line in Slope-Intercept form is:

 $y=mx+b$  

Where "m" is the slope and "b" is the y-intercept.

You can observe in the Equation 1 that the slope of this line is 2 and you can notice in the Equation 2 that the slope of that line is also 2. Therefore, the lines are parallel and the system of equations has no solution.